The Teatotaller is someone from the Temperance movement especially in Ireland. When I visited Ireland several years ago, I saw people in the pubs who wore a pin or badge of a Teatotaller (not sure of the spelling). That is someone who abstains from drinking alcohol. Pubs are a large part of the society in Ireland, so they are for everyone, not just drinkers.
The people you saw who wear the badges are known as “Pioneers”. The pubs are aboslutely for everyone. All one needs to know about the Pioneers may well be found at: http://www.pioneertotal.ie/pioneer/fc?action=index